The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  1  0  1  1  0 a*X  1  1  1 a*X  1  1  1  1  1
 0  1  0  0  0  X  X a^2*X+1 a*X+1  1 a^2*X+a a*X+a a^2 a^2 X+a^2 a^2*X+a  1  1  a  1  1 a*X+a^2  1 X+1  1 a*X+a  a  1 a^2*X X+a
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a a^2*X  a a*X+1  a a^2 a*X+a a^2*X a*X+a^2 a^2*X+a^2 a^2*X+a^2 a^2 X+a^2  0  1 a^2*X+a  0 a^2*X+1 a*X a^2*X+1 a*X+a^2 X+a^2 a*X+a
 0  0  0  1 a^2  a  1 a*X X+a  a  X a*X+a^2  0 a*X+1 a^2 a^2*X+a a^2*X+1  a  0  X X+a^2 a*X+1 a*X+1 a*X+a a^2*X+a a*X+1 a^2 a*X+a^2 X+a^2  1
 0  0  0  0  X  0 a*X  0  0  0  X  X  X a^2*X a*X a*X a^2*X a^2*X a^2*X  X a*X a*X  X a*X a*X  0  0  X  0 a*X

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+168x^74+312x^75+600x^76+948x^77+2136x^78+2532x^79+2601x^80+3828x^81+6288x^82+6576x^83+7374x^84+9864x^85+16176x^86+14328x^87+16977x^88+19272x^89+26184x^90+20040x^91+20889x^92+19812x^93+22008x^94+14340x^95+9843x^96+7236x^97+6912x^98+3312x^99+990x^100+480x^101+57x^104+45x^108+9x^112+6x^116

The gray image is a linear code over GF(4) with n=120, k=9 and d=74.
This code was found by Heurico 1.16 in 86.4 seconds.